Instruction 10-2
a Researcher Randomly Sampled 30 Graduates of an MBA

question 8

Multiple Choice

Instruction 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries.Of primary interest to the researcher was the effect of gender on starting salaries.The result of the pooled-variance t test of the mean salaries of the females (Population 1) and males (Population 2) in the sample is given below.
$$\begin{array}{l}\begin{array} { |l | l| } \hline \text {Hypothesised Difference }&0\\\hline \text {Level of Significance }&0.05\\\hline \text {Population 1 Sample }&\\\hline \text {Sample Size }&18\\\hline \text {Sample Mean }&48266.7\\\hline \text {Sample Standard Deviation }&13577.63\\\hline \text { Population 2 Sample}&\\\hline \text {Sample Size }&12\\\hline \text { Sample Mean}&55000\\\hline \text {Sample Standard Deviation }&11741.29\\\hline \text {Difference in Sample Means }&-6733.3\\\hline \text {-Test Statistic }&-1.40193\\\hline \text {Lower-Tail Test }&\\\hline \text {Lower Critical Value }&-1.70113\\\hline \text { \( p \) -Value}&0.085962\\\hline\end{array}\end{array}$$
-Referring to Instruction 10-2,the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates.According to the test run,which of the following is an appropriate alternative hypothesis?

• A)H₁: ?_females = ?_males
• B)H₁: ?_females > ?_males
• C)H₁: ?_females < ?_males
• D)H₁: ?_females ? ?_males

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Definitions:

Sampling Distribution

A distribution indicating the probabilities of a statistic, which is calculated from a random sample.

Sample Proportion

The fraction of the sample that represents a particular attribute or characteristic.

Normal Probability Distribution

A bell-shaped distribution characterized by its mean and standard deviation, representing a continuous random variable.

Central Limit Theorem

A statistical theory that states that the distribution of sample means approximates a normal distribution as the sample size becomes larger, regardless of the population's distribution.